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The function f(x) = -6x +6 has two real zeros. Choose the correct answer below. O A. The statement is false because f(x)= -6x +6, is of even degree and has a negative leading coefficient. So, the graph of a function is a curve with one end pointing upwards and the another end pointing downwards. So, the graph intersects the x-axis only once. OB. The statement is true because f(x)= -6x +6, is of even degree and has a negative leading coefficient with a negative y-intercept of (0,- 6). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph intersects the x-axis twice. OC. The statement is true because f(x)= -6x +6, is of even degree and has a negative leading coefficient with a positive y-intercept of (0.6). So, the graph of a function is a curve with both ends pointing downwards and the positive y-intercept indicates that at least part of the curve lies above the x-axis. So, the graph intersects the x-axis twice. OD. The statement is false because f(x) = -6x +6, is of even degree and has a negative leading coefficient with a negative y-intercept of (0.-6). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph does not intersect the x-axis.

The function f(x) = -6x +6 has two real zeros. Choose the correct answer below. O A. The statement is false because f(x)= -6x +6, is of even degree and has a negative leading coefficient. So, the graph of a function is a curve with one end pointing upwards and the another end pointing downwards. So, the graph intersects the x-axis only once. OB. The statement is true because f(x)= -6x +6, is of even degree and has a negative leading coefficient with a negative y-intercept of (0,- 6). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph intersects the x-axis twice. OC. The statement is true because f(x)= -6x +6, is of even degree and has a negative leading coefficient with a positive y-intercept of (0.6). So, the graph of a function is a curve with both ends pointing downwards and the positive y-intercept indicates that at least part of the curve lies above the x-axis. So, the graph intersects the x-axis twice. OD. The statement is false because f(x) = -6x +6, is of even degree and has a negative leading coefficient with a negative y-intercept of (0.-6). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph does not intersect the x-axis.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Instructions:** Without graphing, state whether the following statement is true or false. The function \( f(x) = -6x^4 + 6 \) has two real zeros. **Choose the correct answer below:** - **A.** The statement is false because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient. So, the graph of a function is a curve with one end pointing upwards and the other end pointing downwards. So, the graph intersects the x-axis only once. - **B.** The statement is true because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient with a negative y-intercept of \( (0, -6) \). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph intersects the x-axis twice. - **C.** The statement is true because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient with a positive y-intercept of \( (0, 6) \). So, the graph of a function is a curve with both ends pointing downwards and the positive y-intercept indicates that at least part of the curve lies above the x-axis. So, the graph intersects the x-axis twice. - **D.** The statement is false because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient with a negative y-intercept of \( (0, -6) \). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph does not intersect the x-axis.
Transcribed Image Text:**Instructions:** Without graphing, state whether the following statement is true or false. The function \( f(x) = -6x^4 + 6 \) has two real zeros. **Choose the correct answer below:** - **A.** The statement is false because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient. So, the graph of a function is a curve with one end pointing upwards and the other end pointing downwards. So, the graph intersects the x-axis only once. - **B.** The statement is true because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient with a negative y-intercept of \( (0, -6) \). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph intersects the x-axis twice. - **C.** The statement is true because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient with a positive y-intercept of \( (0, 6) \). So, the graph of a function is a curve with both ends pointing downwards and the positive y-intercept indicates that at least part of the curve lies above the x-axis. So, the graph intersects the x-axis twice. - **D.** The statement is false because \( f(x) = -6x^4 + 6 \), is of even degree and has a negative leading coefficient with a negative y-intercept of \( (0, -6) \). So, the graph of a function is a curve with both ends pointing upwards and the negative y-intercept indicates that at least part of the curve lies below the x-axis. So, the graph does not intersect the x-axis.
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